Algebra for Master's in Education: Enhance Your Math Skills

Question 1

To expand the expression (x + 2)^2, what should you do?

Accepted Answer

(a) Multiply (x + 2) by itself

Answer

(b) Square both x and 2

Answer

(c) Add x and 2

Answer

(d) Subtract x from 2

Question 2

To simplify (2x^3)(3x^2), what exponent rule should you apply?

Accepted Answer

(a) Multiply exponents when multiplying terms with like bases

Answer

(b) Add exponents when multiplying terms with like bases

Answer

(c) Subtract exponents when multiplying terms with like bases

Answer

(d) Divide exponents when multiplying terms with like bases

Question 3

Which of the following is NOT a property of equality?

Accepted Answer

Zero is equal to every number (Identity).

Answer

When two quantities are equal to the same quantity, they are equal to each other (Transitive).

Answer

A quantity is equal to itself (Reflexive).

Answer

When two quantities are equal, you can interchange their positions without changing the equality (Symmetric).

Question 4

Simplify the expression: 3x + 5 - 2x - 3

Accepted Answer

x + 2

Answer

2x + 2

Answer

x + 8

Answer

2x + 8

Question 5

Factor the expression: x^2 - 9

Accepted Answer

(x - 3)(x + 3)

Answer

(x - 9)(x + 9)

Answer

(x - 1)(x + 9)

Answer

(x - 9)(x - 1)

Question 6

Expand and simplify: (x + 2)(x - 3)

Accepted Answer

x^2 - x - 6

Answer

x^2 + x - 6

Answer

x^2 - 5x - 6

Answer

x^2 + 5x - 6

Question 7

Solve the inequality: 2x - 5 > 11

Accepted Answer

x > 8

Answer

x < 8

Answer

x > 16

Answer

x < 16

Question 8

What is the slope of the line represented by the equation y = 2x + 3?

Accepted Answer

2

Answer

1

Answer

3

Answer

4

Question 9

What is the shape of the graph generated by a quadratic equation in the form y = ax^2 + bx + c?

Accepted Answer

Parabola

Answer

Hyperbola

Answer

Ellipse

Answer

Line

Question 10

In the algebraic expression 3x + 4, what does the 'x' represent?

Accepted Answer

An unknown number

Answer

A constant value

Answer

An operation

Answer

An equation

Question 11

Which of the following is NOT a property of real numbers?

Accepted Answer

They are not commutative under addition.

Answer

They have an additive identity.

Answer

They are associative under multiplication.

Answer

They are closed under subtraction.

Question 12

Factor the expression: x^2 - 9y^2

Accepted Answer

(x - 3y)(x + 3y)

Answer

(x + 9y)^2

Answer

(x - 3y)^2

Answer

(x - 9y)(x + 9y)

Question 13

**Which of the following is an example of a linear equation?**

Accepted Answer

y = 3x + 1

Answer

y = x³

Answer

y = 1/x

Answer

y = x² + 2x + 1

Question 14

**Which of the following is a solution to the inequality x ≤ -4?**

Accepted Answer

-5

Answer

3

Answer

4

Answer

0

Question 15

**Which of the following expressions represents 'the product of 3 and the sum of x and y'?**

Accepted Answer

3(x + y)

Answer

(3 + x)y

Answer

3x + y

Answer

x + 3y

Question 16

**Factor completely:**
3x² - 12x + 9

Accepted Answer

3(x - 3)²

Answer

(x - 3)³

Answer

3(x + 3)(x - 1)

Answer

(3x - 9)(x - 1)

Question 17

What is the solution set for the inequality 5x - 3 > 17?

Accepted Answer

{x | x > 4}

Answer

{x | x < 4}

Answer

{x | x ≤ 4}

Answer

{x | x ≥ 4}

Question 18

A line has the equation y = 2x + 1. Which of the following points lies on the line?

Accepted Answer

(1, 3)

Answer

(-1, 0)

Answer

(2, 1)

Answer

(0, 2)

Question 19

Simplify the expression: (3x²y⁴) / (xy²)

Accepted Answer

3xy²

Answer

3x/y²

Answer

3xy

Answer

3x³y⁶

Question 20

The cost of renting a car is £30 per day plus £0.20 per mile driven. Which equation represents the total cost (C) of renting a car for 'd' days and driving 'm' miles?

Accepted Answer

C = 30d + 0.20m

Answer

C = (30 + 0.20)dm

Answer

C = 30d / 0.20m

Answer

C = 30m + 0.20d

Question 21

Which of the following is a valid algebraic expression?

Accepted Answer

3x + 5

Answer

x + y = 10

Answer

2x > 7

Question 22

Simplify the expression: 4a + 3b - 2a + 5b

Accepted Answer

2a + 8b

Answer

2a - 2b

Answer

6a + 8b

Answer

6a - 2b

Question 23

Solve for x: 2x - 5 = 11

Accepted Answer

x = 8

Answer

x = -3

Answer

x = 16

Answer

x = 3

Question 24

Which of the following is NOT a solution to the inequality x > 3?

Accepted Answer

2

Answer

3.5

Answer

4

Answer

5

Question 25

What is the value of the expression 3y² - 2y + 1 when y = 2?

Accepted Answer

9

Answer

7

Answer

11

Answer

13

Question 26

A rectangle has a length of 2x + 3 and a width of x - 1. What is the perimeter of the rectangle in terms of x?

Accepted Answer

6x + 4

Answer

2x² + 2x - 3

Answer

2x² + 5x - 3

Answer

4x + 2

Question 27

Which of the following is a factor of the expression x² - 9?

Accepted Answer

x + 3

Answer

x - 1

Answer

x + 1

Answer

x - 2

Question 28

Solve the system of equations: 2x + y = 5 and x - y = 1

Accepted Answer

x = 2, y = 1

Answer

x = 1, y = 2

Answer

x = 3, y = -1

Answer

x = -1, y = 3

Question 29

The equation y = 2x + 3 represents a straight line. What is the slope of this line?

Accepted Answer

2

Answer

-3

Answer

-2

Answer

3

Question 30

Which of the following is NOT a valid method for solving a quadratic equation?

Accepted Answer

Trial and error

Answer

Factoring

Answer

Quadratic formula